Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

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        <div xml:id="echoid-div107" type="section" level="1" n="43">
          <pb o="76" file="0114" n="121" rhead="CHRISTIANI HUGENII"/>
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        <div xml:id="echoid-div112" type="section" level="1" n="44">
          <head xml:id="echoid-head66" xml:space="preserve">PROPOSITIO XXI.</head>
          <note position="left" xml:space="preserve">
            <emph style="sc">De motu</emph>
            <lb/>
            <emph style="sc">IN</emph>
            <emph style="sc">Cy-</emph>
            <lb/>
            <emph style="sc">CLOIDE</emph>
          .</note>
          <p style="it">
            <s xml:id="echoid-s1676" xml:space="preserve">SI mobile deſcendat continuato motu per quælibet
              <lb/>
            plana inclinata contigua, ac rurſus ex pari al-
              <lb/>
            titudine deſcendat per plana totidem contigua, ita
              <lb/>
            comparata ut ſingula altitudine reſpondeant ſingu-
              <lb/>
            lis priorum planorum, ſed majori quam illa ſint
              <lb/>
            inclinatione. </s>
            <s xml:id="echoid-s1677" xml:space="preserve">Dico tempus deſcenſus per minus in-
              <lb/>
            clinata, brevius eſſe tempore deſcenſus per magis
              <lb/>
            inclinata.</s>
            <s xml:id="echoid-s1678" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1679" xml:space="preserve">Sint ſeries duæ planorum inter easdem parallelas horizon-
              <lb/>
              <note position="left" xlink:label="note-0114-02" xlink:href="note-0114-02a" xml:space="preserve">TAB. IX.
                <lb/>
              Fig. 1.</note>
            tales comprehenſæ A B C D E, F G H K L, atque ita ut
              <lb/>
            bina quæque ſibi correſpondentia plana utriusque ſeriei iisdem
              <lb/>
            parallelis horizontalibus includantur; </s>
            <s xml:id="echoid-s1680" xml:space="preserve">unumquodque vero ſeriei
              <lb/>
            F G H K L magis inclinatum ſit ad horizontem quam pla-
              <lb/>
            num ſibi altitudine reſpondens ſeriei A B C D E. </s>
            <s xml:id="echoid-s1681" xml:space="preserve">Dico bre-
              <lb/>
            viori tempore abſolvi deſcenſum per A B C D E, quam
              <lb/>
            per F G H K L.</s>
            <s xml:id="echoid-s1682" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1683" xml:space="preserve">Nam primo quidem tempus deſcenſus per A B, brevius
              <lb/>
            eſſe conſtat tempore deſcenſus per F G, quum ſit eadem
              <lb/>
            ratio horum temporum quæ rectarum A B ad F G ,
              <note symbol="*" position="left" xlink:label="note-0114-03" xlink:href="note-0114-03a" xml:space="preserve">Prop. 7.
                <lb/>
              huj.</note>
            A B minor quam F G, propter minorem inclinationem.
              <lb/>
            </s>
            <s xml:id="echoid-s1684" xml:space="preserve">Producantur jam ſurſum rectæ C B, H G, occurrantque
              <lb/>
            horizontali A F in M & </s>
            <s xml:id="echoid-s1685" xml:space="preserve">N. </s>
            <s xml:id="echoid-s1686" xml:space="preserve">Itaque tempus per B C poſt
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            A B, æquale eſt tempori per eandem B C poſt M B, cum
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            in puncto B eadem celeritas contingat, ſive per A B, ſive
              <lb/>
            per M B deſcendenti . </s>
            <s xml:id="echoid-s1687" xml:space="preserve">ſimiliterque tempus per G H
              <note symbol="*" position="left" xlink:label="note-0114-04" xlink:href="note-0114-04a" xml:space="preserve">Prop. 6.
                <lb/>
              huj.</note>
            F G, æquale erit tempori per eandem G H poſt N G. </s>
            <s xml:id="echoid-s1688" xml:space="preserve">Eſt
              <lb/>
            autem tempus per B C poſt M B ad tempus per G H poſt
              <lb/>
            N G, ut B C ad G H longitudine, ſive ut C M ad H N,
              <lb/>
            cum hanc rationem habeant & </s>
            <s xml:id="echoid-s1689" xml:space="preserve">tempora per totas M C, N H,
              <lb/>
            & </s>
            <s xml:id="echoid-s1690" xml:space="preserve">per partes M B, N G , ideoque etiam tempora reliqua.</s>
            <s xml:id="echoid-s1691" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0114-05" xlink:href="note-0114-05a" xml:space="preserve">Prop. 7.
                <lb/>
              huj.</note>
            Eſtque B C, minor quam G H propter minorem inclina-
              <lb/>
            tionem. </s>
            <s xml:id="echoid-s1692" xml:space="preserve">Patet igitur tempus per B C poſt M B ſive </s>
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